1/(x-1)+1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)+1/(x-4)(x-5)=[(x-2)+1]/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)+1/(x-4)(x-5)=1/(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)+1/(x-4)(x-5)=[(x-3)+1]/(x-2)(x-3)+1/(x-3)(x-4)+1/(x-4)(x-5)=1/(x-3)+1/(x-3)(x-4)+1/(x-4)(x-5)=1/(x-4)+1/(x-4)(x-5)=1/(x-5)
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